Finite Group Databasebeta

C2×#19135663 #25123616

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135663

Splittings

FittingC2×C43×H(3,ℤ/4) ⋊ C2
SylowC43 ⋊ C2×#2010

Subgroups

subgroupG/H
centerC2×C4#13063322
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC22×C43#392
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43C2×#2010
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

2190 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

976 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 196587);